The couples want the court to rule that the state's marriage law is unconstitutional because it applies only to heterosexual couples, effectively denying gay couples the financial, social and emotional benefits of marriage.
"What is denied to these families is something that goes to the heart of equal protection, which is the right to be part of the fabric of society when they are just the same as other couples and other families," said their attorney, Bennett Klein.
Connecticut was the first state to allow civil unions without court pressure, but the lawsuit raises questions of whether the 2005 law helped or hurt same-sex couples in their quest for equality.
As several states consider civil union laws, the Connecticut case could have nationwide implications. Both sides said Monday they are aware of its significance.
"Our 9-year-old said it best: â€˜How is the world supposed to get better if nothing changes?'" said plaintiff Geraldine Artis of Clinton.
Assistant Attorney General Jane Rosenberg, representing the state, argued that civil unions give gay couples the same rights by state law as married couples.
"(The question) is really, is the Legislature constitutionally required to use the word marriage when it's referring to the package of rights and benefits it has given to same-sex couples. And the answer is clearly no," Rosenberg said.
Arguments wrapped up after about three hours Monday, and the justices are expected to rule later this year.
Only Massachusetts allows same-sex couples to marry. Connecticut, Vermont, California, New Jersey, Maine and Washington have laws allowing either civil unions or domestic partnerships, with New Hampshire and Oregon set to join in January. Hawaii extends certain spousal rights to same-sex couples and cohabiting heterosexual pairs.
A theme at Monday's hearing was whether gays and lesbians should be considered a protected group.
That is the legal term for a segment of the population that, among other things, is particularly vulnerable to discrimination and lacks political power.
The Connecticut couples who sued have been together between 10 and 32 years and say civil unions are inferior to marriage and violate their rights to equal protection and due process. Married couples have federal rights related to taxes, Social Security beneficiary rules, veterans' benefits and other laws that people in civil unions don't have. Because civil unions aren't recognized nationwide, other rights, such as the ability to make medical decisions for an incapacitated partner, disappear when couples cross state lines. The couples' claim was dismissed last year by a judge who said they received the equality they sought when Connecticut passed its civil unions law. The couples appealed. The lawsuit names state Department of Public Health and the Madison town clerk's office, which denied marriage licenses to the couples based on state Attorney General Richard Blumenthal's advice. A bill is pending in Connecticut's legislature to approve same-sex marriage, but leaders of the Judiciary Committee say they want to pull it from consideration this session because they do not believe enough lawmakers would vote to approve it. Republican Gov. M. Jodi Rell, who signed the civil unions bill into law, has said she would veto a gay marriage bill. -- Associated Press writer Susan Haigh in Hartford contributed to this report. AP-CS-05-14-07 1732EDT